linbox
Modules | Files | Data Structures | Functions
algorithms

The core linear algebra algorithms of LinBox. More...

Modules

 Chinese Remaindering Algorithm
 Chinese Remaindering (cra) in LinBox.
 
 Diophantine solvers
 NO DOC YET.
 
 Elimination
 NO DOC YET.
 
 Gauss
 NO DOC YET.
 
 IML
 NO DOC YET.
 
 Lanczos
 NO DOC YET.
 
 Lattice reductions
 Lattice reduction (LLL) in LinBox.
 
 Blas3
 BLAS level 3 (matrix-matrix) operations.
 
 p-adic lifting for linear system solutions.
 interface for solving linear system by p-adic lifting technique over the quotient field of a ring.
 
 Sigma-basis
 NO DOC YET.
 
 Wiedemann
 NO DOC YET.
 
 Solvers
 

Files

file  bbcharpoly.h
 no doc.
 
file  blackbox-block-container-base.h
 NO DOC.
 
file  blackbox-block-container.h
 no doc.
 
file  cra-domain.h
 Wrapper around OMP/SEQ version of ChineseRemainder.
 
file  cra-early-multip.h
 NO DOC.
 
file  cra-early-single.h
 NO DOC.
 
file  cra-full-multip-fixed.h
 CRA for multi-residues.
 
file  cra-full-multip.h
 NO DOC.
 
file  cra-givrnsfixed.h
 NO DOC.
 
file  cra-kaapi.h
 NO DOC.
 
file  echelon-form.h
 NO DOC.
 
file  lattice.h
 LLL reductionThis is an interface to NTL/FPLLL.
 
file  lifting-container.h
 Lifting from mod p^n to rationals NO DOC.
 
file  matrix-hom.h
 Matrix Homomorphism A map function converts a matrix on a field/ring to its natural image in another field/ring.
 
file  matrix-rank.h
 Computes the rank of a matrix by Gaussian Elimination, in place.
 
file  rational-reconstruction.h
 NO DOC.
 
file  rational-solver.h
 Rational solving (Dixon, Wiedemann,...)
 
file  rns.h
 Residue Number System tools.
 
file  rns.inl
 Residue Number System implementation.
 
file  short-vector.h
 NO DOCNO DOC.
 
file  smith-form-adaptive.h
 Implement the adaptive algorithm for Smith form computation.
 
file  wiedemann.h
 minpoly computation and Wiedeman solvers.
 
file  linbox-tags.h
 Provides tags for various algorithms/solutions, à la FFLAS.
 

Data Structures

class  BlackboxContainerSymmetrize< Field, _Blackbox, RandIter >
 Symmetrizing iterator (for rank computations). More...
 

Functions

template<class Polynomial , class Blackbox >
Polynomial & cia (Polynomial &P, const Blackbox &A, const Method::BlasElimination &M)
 Algorithm computing the integer characteristic polynomial of a dense matrix. More...
 

Detailed Description

The core linear algebra algorithms of LinBox.

The codes here implement algorithms for linear algebra problems. The names often reflect the authorship of the central algorithm (Lanczos, Wiedemann, ...). In contrast, the "drivers" in the solutions directory are named for the problem solved (rank, det, ...). Those are generally wrappers of algorithms from this directory. Their purpose is to give a simple and direct user interface and sometimes to provide a solution strategy which is a hybrid of algorithms from this directory.

Algorithm classes and functions generally have the field class as a template parameter. Blackbox algorithms may have a BlackboxMatrix parameter or allow a Blackbox class as template parameter. Elimination codes work over DenseMatrix or SparseMatrix types with varying degrees of substitution among the types possible.

Function Documentation

Polynomial& LinBox::cia ( Polynomial &  P,
const Blackbox &  A,
const Method::BlasElimination &  M 
)

Algorithm computing the integer characteristic polynomial of a dense matrix.

Bibliography:
[Dumas-Pernet-Wan ISSAC05]